An Isaac Newton Institute Workshop

Logic and Databases

On the clique-width of graphs

Abstract

Clique-width is a graph parameter that measures in a certain sense the
complexity of a graph. It is known that MSO_1 queries can be evaluated
in polynomial time on classes of graphs with effectively bounded
clique-width. Here MSO_1 denotes the fragment of Monadic Second Order
Logic with second-order quantification on vertex sets. NP-hard
problems like 3-colorability can be expressed as MSO_1 queries.

This talk will survey the concept of clique-width, its advantages and
its limits. In particular, new NP-hardness results for the recognition
of graphs with bounded clique-width will be presented; these results
were recently obtained in joint work with M.R. Fellows, F. Rosamond,
and U. Rotics.